Averaging principle for a class of distribution dependent slow-fast stochastic differential equations driven by fractional Brownian motion and standard Brownian motion

Abstract

This paper investigates a class of distribution dependent slow-fast stochastic differential equations driven simultaneously by multidimensional standard Brownian motions and a multidimensional fractional Brownian motion with Hurst parameter $1/2<H<1$. Existence and uniqueness of the system is proved by using the Picard iteration. Moreover, strong averaging principle is studied to show that slow variable of the system can be efficiently approximated by solution of associated averaged stochastic differential equation.